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Although ordinary heat exchangers may be extremely
different in design and construction and may be of the single-
or two-phase type, their modes of operation and effectiveness
are largely determined by the direction of the fluid flowwithin the exchanger.
The most common arrangements for flow paths within a heat
exchanger are counter-flow and parallel flow. A counter-flow
heat exchanger is one in which the direction of the flow of one
of the working fluids is opposite to the direction to the flow of
the other fluid. In a parallel flow exchanger, both fluids in the
heat exchanger flow in the same direction.
Figure represents the directions of fluid flow in the parallel
and counter-flow exchangers. !nder comparable conditions,
more heat is transferred in a counter-flow arrangement than in
a parallel flow heat exchanger.
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The temperature profiles of the two heat exchangers indicatetwo ma"or disadvantages in the parallel-flow design. First, the
large temperature difference at the ends #Figure $%& causes
large thermal stresses. The opposing expansion and
contraction of the construction materials due to diverse fluid
temperatures can lead to eventual material failure. 'econd, the
temperature of the cold fluid exiting the heat exchanger never
exceeds the lowest temperature of the hot fluid. This
relationship is a distinct disadvantage if the design purpose isto raise the temperature of the cold fluid.
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The design of a parallel flow heat exchanger is advantageous
when two fluids are re(uired to be brought to nearly the same
temperature.
The counter-flow heat exchanger has three significant
advantages over the parallel flow design. First, the more
uniform temperature difference between the two fluids
minimi)es the thermal stresses throughout the exchanger.
'econd, the outlet temperature of the cold fluid can approach
the highest temperature of the hot fluid #the inlet temperature&.
. 'econd, the outlet temperature of the cold fluid can approach
the highest temperature of the hot fluid #the inlet temperature&.
*hether parallel or counter-flow, heat transfer within the heat
exchanger involves both conduction and convection. +nefluid #hot& convectively transfers heat to the tube wall where
conduction takes place across the tube to the opposite wall.
The heat is then convectively transferred to the second fluid.
ecause this process takes place over the entire length of the
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exchanger, the temperature of the fluids as they flow through
the exchanger is not generally constant, but varies over the
entire length, as indicated in Figure $%. The rate of heat
transfer varies along the length of the exchanger tubes
because its value depends upon the temperature difference
between the hot and the cold fluid at the point being viewed.
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The heat transfer coefficient or film coefficient, in
thermodynamics and in mechanics is the proportionality
coefficient between the heat flux and the thermodynamic driving
force for the flow of heat #i.e., the temperature difference, T &
where
q" : heat fux, W/m2 i.e., thermal power per unit
area, q = dQ/dA
h : heat transer coecient, W/(m2•!
T : #i$erence in temperature %etween thesoli# surace an# surroun#in& fui# area,
It is used in calculating the heat transfer , typically by convection
or phase transition between a fluid and a solid.
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The heat transfer coefficient has 'I units in watts per s(uared
meter kelvin */#m01&.
2eat transfer coefficient is the inverse of thermal insulance. Thisis used for building materials #3-value& and for clothing
insulation.
The log mean temperature difference #also known by its
initialism LMTD& is used to determine the temperature driving
force for heat transfer in flow systems, most notably in heat
exchangers. The 45T6 is a logarithmic average of the
temperature difference between the hot and cold streams at each
end of the exchanger. The larger the 45T6, the more heat is
transferred. The use of the 45T6 arises straightforwardly from
the analysis of a heat exchanger with constant flow rate and
fluid thermal properties.
'ontents
e)nition
*e assume that a generic heat exchanger has two ends #which
we call 7A7 and 77& at which the hot and cold streams enter or
exit on either side8 then, the 45T6 is defined by the logarithmic
mean as follows
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where ΔT A is the temperature difference between the two streams
at end A, and ΔT B is the temperature difference between the two
streams at end B. *ith this definition, the 45T6 can be used to
find the exchanged heat in a heat exchanger
*here Q is the exchanged heat duty #in watts&, U is the heat
transfer coefficient #in watts per kelvin per s(uare meter& and Ar
is the exchange area. 9ote that estimating the heat transfer
coefficient may be (uite complicated.
This holds both for cocurrent flow, where the streams enter from
the same end, and for counter-current flow, where they enter
from different ends.
In a cross-flow, in which one system, usually the heat sink, has
the same nominal temperature at all points on the heat transfer
surface, a similar relation between exchanged heat and 45T6
holds, but with a correction factor. A correction factor is also
re(uired for other more complex geometries, such as a shell and
tube exchanger with baffles.